There’s something right about the argument Edlin et al are making; it being rational for you to vote does require a degree of altruism. But I think their model (a) makes some fairly heroic assumptions, and more importantly (b) doesn’t explain why so many people in America should go vote today. Below the fold I give a slightly different reason for voting, one that applies in all 50 American states. The short version is that you should vote today because it increases your chances of getting a good outcome next time.
For purely selfish people, voting is a bizarre act. You spend a lot of time, energy and (in some cases) money for a vanishingly small chance at improving your lot in life. If you’re an altruist, as Edlin et al point out, it is a little more rational. You spend a lot of time, energy and money for a vanishingly small chance at improving the lot in life of billions of people. Provided you give enough weight to the utility of others, perhaps this could be rational.

But it isn’t clear that it is. It depends on how vanishingly small the chance of making a difference is. Some people are in states where the probability that they are the marginal vote is literally one in billions. (New York and Utah are examples of this.) Many of those people live in states where the probability that their state is the marginal state is also rather high. The probability of being the marginal vote in a marginal state is, for most people, very small. So the model suggested only gives you a reason to vote in close elections.

Indeed, Andrew Gelman in a post about last year’s local elections says that he didn’t vote because the races weren’t close. I think there’s a reason to vote even in races that aren’t that close, and where you don’t give any positive probability to being the marginal vote. (In the currently popular lingo in philosophy, your probability that you are the marginal vote may be vague over an interval including zero.)

Voting is a lot like playing an n-player Prisoners Dilemma with the other people who (loosely speaking) share the values that underlie your vote. I’m taking values to be defined loosely enough here that it includes most people who vote the same way you do. You’d prefer that all of you vote to all of you not voting. Given turnout rates in the U.S., that’s pretty much always the difference between winning and losing. But conditional on what the other people will almost certainly do, you’d prefer to not vote than to vote. And so would everyone else. We have a Prisoners Dilemma here, and the rational thing to do in a Prisoners Dilemma is to not cooperate.

Note that we can’t get out of the Prisoners Dilemma merely by assuming altruism. As Simon Blackburn pointed out a while ago (“Practical Tortoise Raising”, Mind 1995), as long as there are any divergences in preferences, even altruists will be in Prisoners Dilemma situations from time to time. And perfect convergence in preferences is a crazy assumption. So real-life Prisoners Dilemmas for moderate altruists are possible. And I think elections are such possibilities.

But wait! There is more than one election. If any election is a Prisoners Dilemma, then a series of elections over time is a repeated Prisoners Dilemma. And one of the things we know for sure is that in repeated 2 player Prisoners Dilemma, the rational thing to do is to cooperate. That’s true even though the short-term benefits from non-cooperation clearly outweigh the benefits of cooperation. So all we need to do is to show that n player Prisoners Dilemmas are the same, and we’ll have an argument for the rationality of voting.

This last step isn’t completely obvious. In the 2 person case, cooperation is required at turn t because otherwise the other player will have a bad attitude towards you, and hence not cooperate at turn t+1. But in the n-player case, few people will know that you haven’t voted, and fewer still will have their future behaviour effected by this. This isn’t quite true for parents of impressionable children, or perhaps for friends of people who are apathetic/economists, but we might worry it is true of a lot of people.

But there may be another effect of voting. It might be that the probability that others like you will vote in the next election is a more-or-less continuous function of the number of people like you who vote in this election. This doesn’t seem too implausible actually. If we imagine Democrats having received tens of millions fewer votes in 2000 and 2004, then it is hard to imagine the level of support and work for Democrats in this cycle that there actually are. If you imagine the prior Democratic vote being a little closer to actuality, but still down, it is easy to imagine support and enthusiasm levels this time being down.

If I were being more careful here, I’d try to work out the marginal efficiency of voting at producing future votes. That is, the marginal difference that an extra vote for your team in this election makes to the expected number of votes your team gets in subsequent elections. I suspect it is well over 1. That’s because dropping a party’s support by a lot, say 10,000,000 in a US context, feels like it could be so demoralisingly bad that the party struggles to recover. But this would need a lot more work. It is certainly easy to come up with not completely crazy looking mathematical models where the efficiency is over 2. If everyone like you is a little demoralised by your not voting, even if it’s just a very little bit, that could easily translate into votes lost next time.

Moreover, that effect need not be localised. It’s pretty unlikely that New York will be a swing state any time soon. It’s unlikely that it will be close, and conditional on it being close, it’s unlikely that the national race will be close. But cross-voter incentives can work across state lines. People pay attention to what the national popular vote number is, and it effects their marginal disposition to vote/campaign for candidates that you like. So a vote in New York now may translate into benefits in swing states (which probably means the Mountain West) in the future.

So I think there’s a reason for rational altruists to vote, even when they know they won’t be the marginal vote. They are signaling to like-minded voters that they will vote, and that’s crucial for sustained success. This isn’t an alternative to Edlin et al’s model. In fact I think they are right that someone with no other-related preferences shouldn’t vote, even given the dynamic effects of voting described here. But I think the dynamic effects (a) make the case for voting considerably stronger, and (b) explain why it is rational to vote even in states that won’t be close, and won’t be swing states if they are close.

In any case, I don’t think any readers of this blog have no other-related preferences. You should all go vote, as a signal to everyone else that you’re voters. Take my advice, and you’ll thank me in 2012. You really are voting for America’s future; if I’m right most people in the country are largely voting for America’s electoral future.

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Why most people actually vote and why most people should vote are two entirely different questions.

My (pop sociological) sense of why most voters vote is that it’s a combination of: a) a sense of civic duty (i.e. ideology) and b) devotion to their own party and its candidate plus resentment or disgust toward the other major party and its candidate (i.e. voting as an expressive act). Very few voters are making any sort of “rational” calculation that their individual vote will make a difference.

As for why people should vote….Any serious analysis needs to take into account the many ways in which vote totals are used in our political life for things beyond simply determining a winner and a loser. That is: a landslide victory is a different thing from a one-vote win. And the impact of the size and shape of an electoral victory goes far beyond their direct effects on the next iteration of the “game.” One’s individual vote still makes a very small difference, but its very small difference cannot be reduced to the vanishingly small chance that it will be the marginal vote.

Is this true? I don’t spend a lot of time, energy or money voting – my polling station is round the corner, it’s rarely been more than 10 minutes walk from wherever I lived, and I’ve never had to queue.

I appreciate that this is different for some people, but if all analyses of voting and why people do it starts with the assumption that it is a cumbersome and difficult act, then they are way off.

If any election is a Prisoners Dilemma, then a series of elections over time is a repeated Prisoners Dilemma. And one of the things we know for sure is that in repeated 2 player Prisoners Dilemma, the rational thing to do is to cooperate.

Not quite. The most successful demonstrated strategy is “tit for tat”: cooperate with the cooperative, defect when playing with a past defector. Of course, this is incoherent when applied to an n-player game where n > 2: some people voted last time, but some did not. So should I vote or not this time around if I want to maximize my utility?

This is why rational people still come down on either side of this question. (Just don’t admit that you’re one of the people not voting in the comments section at Crooked Timber; the rest of the peanut gallery will call you a scoundrel.)

An interesting upshot of this argument is that it makes a difference for how you should vote. The argument only rationalizes votes in accordance with an enduring set of values that a decent number of other voters share. So, for instance, votes based on quirks of a particular candidate’s personality (even if you think they’re quite important quirks) aren’t justified on these grounds.

and the rational thing to do in a Prisoners Dilemma is to not cooperate.

Actually, in a Prisoner’s Dilemma cooperation is strictly impossible. Whether or not it’s rational to make one choice or the other is dependent on the expected value of each, and I think if you total up all the ballot initiatives and candidates for which you can vote in an election, it is not obvious that the expected value of doing nothing exceeds the expected value of voting. Not without some more rigorous math on the “vanishingly small” chance that my vote will be the tie-breaker for a school referendum or a particular judge’s race.

“My heart was so full after voting I found that I could scarcely breathe.”

2. Since it is only possible to experience a nation through ritual performances of its existence, then those rituals matter: do you really think obam winning by 6 votes to ten is remotely the same thing as him winning by 78 million to 52 million?

I must be missing something about a key argument of that original article–and this rewording of it:

“You spend a lot of time, energy and (in some cases) money for a vanishingly small chance at improving your lot in life.”

This seems line of reasoning seems deeply flawed. The probable effectiveness of a single vote depends, not on the individual vote, but on the probability of others voting in the same way. So the “vanishingly small chance” claim makes the mistake of not factoring the latter probability into the equation.

It’s as if I said: I have a vanishingly small chance of single-handedly pushing a stranded motorist’s minivan out of traffic on my own strength, therefore I don’t have an incentive to try to get others to help me push a stranded motorist’s minivan off the road with our shared strength. The strength of my individual action differs according to whether it’s shared, so we can’t measure it in isolation. Maybe it’s not surprising that economists would reason this way–it’s a distorted, atomistic picture of reality, of cause and effect, and, above all, of human relations. Precisely the kind that can speak without snickering in the puzzling, paradoxical, possible non-sensical language of an polar opposition of self interest and altruism. (In this polarized sense, not one concrete example of action qualifying as truly self-interested or truly other-interest can be given as evidence of the meaningfulness of the terms.)

I have a vanishingly small chance of improving my lot by voting only if there’s a vanishingly small chance that a majority of people will vote the same way. Fortunately, that’s rarely the case.

People vote because cultural groups and organizations which encourage their members to vote wield disproportionate power and reap disproportionate rewards in society. These cultural groups thus become more powerful and tend to grow larger and spread their pro-voting memes. They do so by providing their members with enhanced self-esteem for group-related activities including voting, which is the most powerful motivator of human behavior. (Monetary wealth is a subset of self-esteem and social standing, not the other way around.) Meanwhile, cultural groups which are apathetic towards voting lose political power, fail to reproduce their memes, and tend to tail off towards irrelevance or nonexistence.

The problem for the economists listed above is that they identify the individual as the unit of choice. Human beings do not behave that way. They make most decisions in groups.

I’d like to point out that you’re double-counting your probabilities in arriving at your “vanishingly small” chance of affecting the outcome. The way your state votes is significant any time the election outcome would be different if your state voted the other way. So we don’t care if New York is a “swing state” when deremining if it impacts the election. What we care about is if the electoral-vote margin is less than New York’s electoral vote total. If so, New York’s outcome determined the national outcome and your chance of affecting the national outcome is exactly equal to your chance of affecting the state’s support. That number may be vanishingly small, but the math that connects it to the national number is based on the probability of an electoral split being less than 62 electoral votes apart in New York’s case. Whether or not New York is a “swing state” depends on the expected vote distribution within the state, which is just another way to count your chance of affecting where New York’s electoral votes fall.

>> You spend a lot of time, energy and (in some cases) money for a vanishingly small chance at improving your lot in life.
>>>> What? I just voted and it took all the time and energy of running to a coffee shop and cost nothing.

The point being, if you do not spend a *lot* of time and energy on voting, your vote is correspondingly less valuable to you, under the “common sense” rule that more effort equates to more value.

So you better work yourself up into thinking that a walk to the coffee shop for zero cost is a huge effort on your part. About as much as standing in a line and ticking one box on one paper once, or you will end up convincing yourself that you don’t matter at all. Because otherwise you will have to face the fact that the tough part of the job is choosing which box to tick. On your own. With no TV to persuade you. Or the Internet.

I agree entirely with some of the comments, especially Daniel Rosenblatt, that a lot of people should vote because they will get psychological benefits from it. Frankly, that’s why I’ve done a little campaign work – if I had done none at all I wouldn’t feel as much a part of the victory. Maybe that’s explanation enough for a lot of people.

But I don’t think I’m double counting the relevant probabilities. I think the probability that your vote matters is the probability that (a) you’ll be important to how your state votes and (b) how you’re state votes is relevant to the overall result. And it’s worthwhile to note that as low as (a) is, the conditional probability of (a) given (b) is even lower still.

it is only possible to experience a nation through ritual performances of its existence, then those rituals matter

but what experience do you have of a nation? Aren’t you imagining the community anyway? In which case, you can do that any time, can’t you?
I’m really not sure that arguments of collective effervescence work on the scale of the nation state.

Brian at 4: a landslide victory doesn’t necessarily predict what kind of government we will have much differently than a one vote victory, but it says a lot of about the people of the population.

I know I will feel a lot better about my country, it’s people and what will come in the next 4-16 years if Obama wins a landslide vs. a one-vote squeaker.

Before 2002, I had strong political preferences, but didn’t always feel like my vote meant much, mostly because I was always choosing a lesser evil.

Ah those were the days. Today, I’m voting a straight democratic ticket, just like I did in 2003, 2004, 2005 and 2006, and just like I will *every* single year until either the Republican party repudiates fascism and racism in its ranks or some other party rises up to take its place (or heaven forfend, democrats as a whole actually stoop close to their level). Republicans don’t just deserve to lose, they deserve to be crushed. They deserve to lose their automatic place on ballots. This is surely how people like me felt in 1976, and I think if they’d known the ghost of Nixon would be back in 30 years to stain our national reputation so much more than I’d ever thought possible, they might have still had that fervor in 1980 and beyond.

The thing I realized this election is that we’re still fighting the civil war. It’s just a cold war now. Like 1964, this will be a big victory, but it’s hardly over, as the outrageous racism, sexism and xenophobia in this campaign and the 40%+ of people willing to vote for it have shown. But we may finally have amassed the coalition to enact the civil rights act and not forfeit 40 years of political power to racist dog-whistlers. That, IMO, is what this election is about. And a 10% margin in the popular vote will make that statement a whole lot louder than a 2% margin.

Quibble: in determining the marginal effect of your vote at t on others’ votes at t+1, t+2, etc., you should take into account the fact that it will probably motivate some people to vote against your guy (or girl) next time around. It seems entirely possible that the effects in each direction could come close to canceling each other out.

Of course, you might think that there’s value in increasing turnout independently of who people end up voting for (particularly if you don’t necessarily assume that you’re 100% likely to have picked right this time around). But that’s a rather different character of argument.

CK Dexter Haven: your analogy might be more apt if you imagined the effect of your trying to pushing the car out of traffic when there are already a few million people pushing on it in opposite directions. In this case, the effect of your trying to push it one way or another is actually likely to be pretty minimal.

2. Since it is only possible to experience a nation through ritual performances of its existence, then those rituals matter: do you really think obam winning by 6 votes to ten is remotely the same thing as him winning by 78 million to 52 million?

Around these parts wouldn’t winning by 6 votes to ten be only something Republicans would be allowed to get away with?

I don’t understand why voting to increase the number of votes your side gets in future elections is more rational than voting to increase the chance that your side wins the current election. It seems to me that the same kind of free rider scheme makes sense – one or two extra votes for my side in the next election is around as unlikely to determine that election as my vote now is to determine this election. Even if those extra votes compound over elections, it’s not obvious to me that there’s much of a payoff. Am I misunderstanding something?

It also occurs to me that one problem with looking at voting as a Prisoner’s Dilemma game is that preferences diverge so much that some people’s payoff matrices aren’t typical of Prisoner’s Dilemmas. A lot of people vote because they see it as a civic duty or as a positive good in its own right. You can defect on these people all day and they’ll happily trudge back to the polls next November – for them, the expected value of voting is almost entirely independent of the likelihood that their vote will make a difference or of what other people do.

You say “I think the probability that your vote matters is the probability that (a) you’ll be important to how your state votes.”

There’s still seems to be a logical problem here, since the the class of how a state votes depends on the the individual votes that comprise the class. The probable value of individual votes cannot directly depend on “how your state votes” since it partially causally determines how the state votes. So we need more sophisticated logical syntax to express what may be, after all, a reasonable point: that if (besides me) a majority of plus two or more will vote one way, there’s no reason for me to add another vote to the pile.

I’m still not finding this satisfying, since it sounds artificial: I don’t really have a way of evaluating the probability that my vote is the majority plus third on the pile. Or, in Conchis’ example: it would be analogous to if I had to decide whether or not to help push, but the number (if any) of other people who are pushing either way won’t be revealed to me until _after_ I’ve decided.

Another issue I didn’t see mentioned is that in some states, there’s a lot more than one issue on the table. To take the most personal example, California will almost certainly go for Obama, so if that were the only contest I cared about, I could probably stay home and my one missing vote wouldn’t really make a big difference. But we also have a dozen ballot initiatives to vote on, several of which are extremely noxious (most notoriously Prop. 8, but Prop. 4 and some of the law ‘n’ order ones aren’t any better). And for many of those elections, the contest is much, much closer, so my vote, as well as that of every other potential voter, makes a much bigger difference.

Brian, you’re absolutely right that the probability that your vote matters is the probability that you affect your state multiplied by the probability that your state affects the election, but I think you mis-stated and misunderstood what it means for your state to influence the election. When you talk about swing states, you’re talking about a completely different animal than when you talk about whether or not your state affects the outcome of the election. Specifically, swing states are states where their effect on the election is hard to predict. But taking 2004 as an example, because Bush won with 286 electoral votes, any red state with more than 16 electoral votes, had it voted the other way, would have changed the outcome of the election, and that’s just as true for deep-red, guaranteed states as it is for swing states that happened to break red. The way you account for the difference between swing states and more deeply partisan states is by looking at the first number, the likelihood that you will affect the outcome of your state.

So the reason I said you were double counting is because you incorrectly characterized your second number, the likelihood that your state influences the outcome of the election. It has nothing to do with swing-statehood and everything to do with how the electoral votes split in absence of your state.

Not that that applies in this election. But in many of them it does. I don’t know why people freak out over this. There are elections in which you should/would want to vote and there are elections where it’s better to stay at home and play video games.